Here's one possible solution, using a variation of the technique used in this answer to How to emulate titletoc with tocloft:
\documentclass{book}
\usepackage{etoolbox}
\newlength\rightmargintoc
\setlength\rightmargintoc{\linewidth}
\addtolength\rightmargintoc{-3em}
\makeatletter
\def\subsubsectocline#1#2#3#4#5{%
\parshape 2 0em \rightmargintoc \dimexpr\parindent\relax \rightmargintoc
\@tempdima#3
\ifdim\lastskip=1sp\relax\ \else\par\fi{\small\itshape#4,~p.#5.}\hskip1sp%
}
\renewcommand*\l@subsubsection{\subsubsectocline{2}{0em}{3em}}
\makeatother
\pretocmd{\part}{\addtocontents{toc}{\par}}{}{}
\pretocmd{\chapter}{\addtocontents{toc}{\par}}{}{}
\pretocmd{\section}{\addtocontents{toc}{\par}}{}{}
\pretocmd{\subsection}{\addtocontents{toc}{\par}}{}{}
\AtEndDocument{\addtocontents{toc}{\par}}
\begin{document}
\addtocontents{toc}{\setcounter{secnumdepth}{2}}
\tableofcontents
\part{Test Part One}
\chapter{Test Chapter}
\section{Test Section One}
\subsection{Test Subsection One One}
\subsubsection{First Test Subsubsection}
\subsubsection{Second Test Subsubsection}
\subsubsection{Third Test Subsubsection}
\newpage
\subsubsection{Fourth Test Subsubsection}
\subsection{Test Subsection One Two}
\subsubsection{First Test Subsubsection}
\subsubsection{Second Test Subsubsection}
\subsubsection{Third Test Subsubsection}
\part{Test Part One}
\chapter{Test Chapter}
\section{Test Section One}
\end{document}
The resulting ToC:
